FBI agents probing the murder of a Staten Island mom in Turkey said they don’t believe she was there just to take pictures — and said she hung out with a “criminal element” during the solo trip abroad.

“There are a lot of open questions that need to be answered,” a source familiar with the ongoing case told The Post.

Mother of two Sarai Sierra, 33, was found dead from a ferocious blow to the skull in a seedy area of Istanbul last Saturday after failing to show up for a Jan. 21 flight home to New York.

“The first people she met up with were a criminal element,” the source said of Sierra, who flew to Turkey Jan. 7, then to Amsterdam on Jan. 15 and Munich on Jan. 16 before heading back to Istanbul Jan. 19.

The FBI is in Turkey investigating the case, and is looking into a possible connection to drug trafficking — among other lines of inquiry, a source said.

“There are some witness reports that she was seen with sketchy characters,” said the source, adding that agents are following up those leads to determine if they’re accurate.

Sierra’s friends and family said the young mom — an amateur photographer who shot her pictures with an iPad and Droid phone — went abroad to take pictures.

During her trip, Sierra planned to connect with friends she’d met online. But the feds aren’t convinced they’re getting the full story of why she was overseas, a source said.

Sierra’s relatives — including husband Steven and brother David Jimenez, who flew to Istanbul last week — are being “cooperative,” sources close to the probe said.

But “being cooperative and being helpful are two different things,” said one source.

Sierra’s family has said she went alone on her first trip abroad after a friend bailed out at the last minute.

The friend, Maggie Rodriguez, told The Post that Sierra began planning the trip “a few months ago” and that she alerted Sierra early on that she couldn’t afford to go with her.

But the previously unemployed Sierra, who declared bankruptcy in 2005, forged ahead.

“Sarai always wanted to go overseas — this time it managed to present itself in a way that she was able to go,” Rodriguez said.

Two churches raised the money for Sierra’s cash-strapped husband, who works as a city bus driver, and brother to travel to Istanbul.

The family yesterday was selling Sarai’s Instagram photos online to raise funds to ship her body home and pay for her funeral. Her husband and brother are slated to return to Staten Island with her body this week.

Sierra told friends she planned to stay overseas for three full weeks, but after 12 days, posted online that she “sadly” had to cut the trip short.